Cluster Stability - Similarity Index and Pattern-wise Stability Approaches
cls.stab.opt.assign reports validation measures for clustering results. Both functions return lists of
cluster stability results computed according to similarity index and pattern-wise stability approaches.
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integer number which tells how many pairs of data subsets will be partitioned for particular number of clusters.
The results of partitioning for given pair of subsets is used to compute similarity indices (in case of
a number comming from (0,1) section which tells how big data subsets should be. 0 means empty subset, 1 means all data.
string vector with names of cluster algorithms to be used. Available are:
"agnes", "diana", "hclust", "kmeans", "pam", "clara". Combinations are also possible.
string vector with information useful only in context of "agnes" and "hclust" algorithms . Available are:
"single", "average", "complete", "ward" and "weighted" (for more details see
string vector with information useful only for
logical argument which sets the way of computing cluster stability for hierarchical algorithms. By default it is set to
TRUE, which means that each result produced by hierarchical algorithm is partitioned for the number of clusters chosen in
additional parameters for clustering algorithms. Note: use with caution! Different clustering methods chosen in
Both functions realize cluster stability approaches described in Detecting stable clusters using principal component analysis (see references).
cls.stab.sim.ind function realizes algorithm given in chapter 3.1 where only cosine similarity index (see
is introduced as a similarity index between two different partitionings. This function realize this cluster stability approach also for other
similarity indices such us
The important thing is that
similarity index (if chosen) produced by this function is not exactly the same as index produced by
similarity.index function. The value of the
similarity.index is a number which depends on number of clusters.
Eg. if two "n-clusters" partitionings are compared the value always will be a number which belong to the
[1/n, 1] section. That means the
results produced by this similarity index are not comparable for different number of clusters. That's why each result is scaled thanks to
the linear function
f:[1/n, 1] -> [0, 1] where "n" is a number of clusters.
The results' layout is described in Value section.
cls.stab.opt.assign function realizes algorithm given in chapter 3.2 where pattern-wise agreement and
pattern-wise stability was introduced. Function returns the lowest pattern-wise stability value for given number of
clusters. The results' layout is described in Value section.
It often happens that clustering algorithms can't produce amount of clusters that user wants. In this situation only the warning is produced and cluster stability is computed for partitionings with unequal number of clusters.
The cluster stability will not be calculated for all cluster numbers that are bigger than the subset size.
For example if
data contains about 20 objects and the
subset.ratio equals 0.5 then the highest cluster number to
calculate is 10. In that case all elements above 10 will be removed from
cls.stab.sim.ind returns a list of lists of matrices. Each matrix consists of the set of external similarity indices (which one similarity
index see below) where number of columns is equal to
cl.num vector length and row number is equal to
rep.num value what means
that each column contain a set of similarity indices computed for fixed number of clusters.
The order of the matricides depends on three input arguments:
method.type give a names for elements listed in the first list. Each element of this list is also a
list type where each element name correspond to one of similarity index type chosen thanks to
The order of the names exactly match to the order given in those arguments description. It is easy to understand after considering the
Let say we are running
cls.stab.sim.ind with default arguments then the results will be given in the following order:
cls.stab.opt.assign returns a list of vectors. Each vector consists of the set of cluster stability indices described in
Detecting stable clusters using principal component analysis (see references). Vector length is equal to
cl.num vector length what
means that each position in vector is assigned to proper clusters' number given in
The order of the vectors depends on two input arguments:
method.type. The order of the names exactly match to the order
given in arguments description. It is easy to understand after considering the following example.
Let say we are running
c("pam", "kmeans", "hclust", "agnes") as
method.type then the results will be given in the following order:
A. Ben-Hur and I. Guyon Detecting stable clusters using principal component analysis, http://citeseerx.ist.psu.edu/
C. D. Giurcaneanu, I. Tabus, I. Shmulevich, W. Zhang Stability-Based Cluster Analysis Applied To Microarray Data, http://citeseerx.ist.psu.edu/.
T. Lange, V. Roth, M. L. Braun and J. M. Buhmann Stability-Based Validation of Clustering Solutions, ml-pub.inf.ethz.ch/publications/papers/2004/lange.neco_stab.03.pdf
Advanced cluster stability functions:
Functions that compare two different partitionings:
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# load and prepare data library(clv) data(iris) iris.data <- iris[,1:4] # fix arguments for cls.stab.* function iter = c(2,3,4,5,6,7,9,12,15) smp.num = 5 ratio = 0.8 res1 = cls.stab.sim.ind( iris.data, iter, rep.num=smp.num, subset.ratio=0.7, sim.ind.type=c("rand","dot.pr","sim.ind") ) res2 = cls.stab.opt.assign( iris.data, iter, clust.method=c("hclust","kmeans"), method.type=c("single","average") ) print(res1) boxplot(res1$agnes.average$sim.ind) plot(res2$hclust.single)
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